Abstract. In the paper it is proved that the generalized linear boundary value problem generates a Fredholm operator. Its index depends on the number of boundary conditions. The existence results of Landesman-Lazer type are given as an application to nonlinear problems by using dual generalized boundary value problems.
AMSclassification. 34B10, 34B15, 47A53
Keywords. Fredholm mapping, generalized BVP, dual problem, bounded nonlinearity, Landesman-Lazer conditions